IK solvers

IK solvers are the mathematical algorithms behind the IK handles. IK solvers calculate the rotations of all the joints in
a joint chain controlled by an IK handle. The effect an IK handle has on a joint chain depends on the type of IK solver used
by the IK handle. By default, Maya loads the following IK solvers on start-up:

If you want to pose and animate joint chains that have between two and four joints, use single chain or rotate plane IK. If
you want to pose and animate longer joint chains, use spline IK. If you want to pose and animate simple three joint IK chains
for use in games, use 2 bone IK.

By default, each IK handle you create that uses the same type of IK solver, also shares the same IK solver node. For example,
all IK handles that use single chain IK also connect to the same ikSCsolver node. Consequently, if you edit the attributes
of the shared IK solver node, all the IK handles that connect to the node are affected. If you want to fine-tune the IK solvers
for certain IK handles only, while not affecting other IK handles, you can create additional IK solvers for your IK handles
using the createNode MEL command.

IK solver calculations

When you move an IK handle, the solver performs the appropriate calculations to move and rotate all the joints in its IK chain
accordingly. First, the solver looks at the position (Translate X, Y, and Z attributes) and orientation (Rotate X, Y, and Z attributes) of the IK handle. Next, the solver calculates how to move the position and orientation of the end effector as
close to the IK handle’s position and orientation as possible. To do that, the solver calculates how to best rotate the joints
in the IK handle’s joint chain. Finally, the solver then rotates all the joints in the joint chain so that the end effector
reaches the IK handle’s position and orientation.

Single Chain solver

A single chain IK handle uses the single chain solver to calculate the rotations of all the joints in the IK chain. Also,
the overall orientation of the joint chain is calculated directly by the single chain solver.

Difference between single chain and rotate plane IK handles

The difference between a single chain IK handle and a rotate plane IK handle is that the single chain IK handle’s end effector
tries to reach the position and the orientation of its IK handle, whereas the rotate plane IK handle’s end effector only tries
to reach the position of its IK handle. Since the rotate plane IK handle’s end effector only tries to reach the position of
its handle, the resulting joint rotations are more predictable. For the rotate plane IK handle, the orientation of its entire
joint chain is controlled by the twist disc manipulator. For more information, see Twist disc and Rotate Plane solver.

Note

If your joint chain suffers from flipping, use the rotate plane solver instead of the single chain solver. The rotate plane
solver was introduced with the pole vector to control the flipping of IK chains that you sometimes get with the single chain
solver.

Single Chain IK handle components

Rotate Plane solver

A rotate plane IK handle uses the rotate plane solver to calculate the rotations of all the joints in its IK chain, but not
the joint chain’s overall orientation. Instead, the IK rotate plane handle gives you direct control over the joint chain’s
orientation via the pole vector and twist disc, rather than having the orientation calculated by the IK solver. The single
chain solver and rotate plane solver differ in this respect. See Difference between single chain and rotate plane IK handles.

The rotate plane solver is ideal for posing joint chains (such as arms and legs) that you want to stay in the same plane.
For example, the shoulder, elbow, and wrist joints of an arm driven by a rotate plane IK handle all stay within the same plane
as the elbow rotates. The plane itself can be rotated from the shoulder joint by the pole vector. See Pole vector and Twist disc.

Rotate Plane IK handle components

Twist disc

The twist disc is a manipulator that you can use to twist or rotate the joint chain. The twist disc is located at the end joint of the IK chain.

Translating the pole vector often leaves the IK chain pointing in the wrong direction. You can use the twist disc to re-orient
the plane after you move the pole vector to prevent flipping. To view an image of the twist disc, see Rotate Plane solver.

Joint chain plane

The joint chain plane is the plane that contains all the joints in the joint chain and poses through the axis. The joint chain
plane rotates about the handle vector. When you manipulate the pole vector, you are rotating the joint chain plane about the
handle vector. To view an image of the joint chain plane, see Rotate Plane solver.

Reference plane

For the joint chain plane to rotate and twist the joint chain, the plane must rotate relative to some other plane so that
the degree of twist can be measured. The plane that the joint chain plane rotates relative to is the reference plane. To view an image of the reference plane, see Rotate Plane solver.

Pole vector

The pole vector is a manipulator that lets you change the orientation of the IK chain. The pole vector also lets you control
flipping.

Since moving the pole vector changes the orientation of the reference plane, moving the pole vector can also change the orientation
of the joint chain directly; just as manipulating the twist disc can change the orientation of the joint chain. This is because
the joint chain’s degree of orientation—or twist—is defined as the difference in orientation between the reference plane and the joint chain plane. To view an image of the
pole vector, see Rotate Plane solver.

Warning

When positioning your IK handle, if the handle vector and the pole vector cross each other or point in exact opposite directions,
the joint chain can suddenly flip. You can prevent this flipping by moving the pole vector so that the handle vector does
not cross it or point in the opposite direction from it.

Rotation disc

The rotation disc is an indicator that displays how much the IK chain has been rotated by the twist disc. The rotation disc
is located at the start joint of the IK chain. To view an image of the rotation disc, see Rotate Plane solver.

Reference plane indicator

The reference plane indicator is the green dot on the rotation disc that moves to reflect the movements of the pole vector.

Twist indicator

The twist indicator is the green arc between the reference plane indicator and the joint chain plane indicator on the rotation
disc. The twist indicator displays the orientation of the joint chain relative to the reference plane.

Joint chain plane indicator

The joint chain plane indicator displays the orientation of the joint chain plane relative to the reference plane. The joint
chain plane indicator appears in the rotation disc.

Spline IK solver

Spline IK handles let you pose a joint chain using a NURBS curve. When you manipulate the curve, the handle’s spline IK solver
rotates the joints in the chain accordingly. You can use spline IK to pose and animate long, sinuous joint chains such as
those for a tail, a tentacle, a snake and so on.

Spline IK handle components

The roll disc is a manipulator that lets you roll or rotate the entire spline Ik joint chain. The roll disc is always at the
spline IK handle’s start joint. The roll disc is similar to the rotation disc and pole vector. See General IK handle components.

Advanced spline IK controls

With the spline IK twist control attributes, you can constrain the local rotation of the joints in a chain to a fixed worldspace
vector. This vector is the orientation of the spline IK NURBS curve. For example, you can use the advanced spline IK twist controls
to stabilize a snake character, the spine of a biped character, or the movements of a coil spring. Also, to fine-tune the
twist along the chain, you can add additional twist to the joints with the Twist Value attributes.

By aligning the joints Up axes with a fixed worldspace vector before applying additional twist, you can achieve a more predictable
and stable result than was previously possible.

The Advanced Twist Control attributes are relevant only if your IK handle uses the ikSplineSolver.

IK handles with spline IK let you pose your joint chains using NURBS curves. When you manipulate the spline IK curve, you
are moving and rotating all the joints in the target IK chain. An easy way to manipulate the spline NURBS curve is to create
a cluster deformer for each of the curves CVs. See Edit Curves > Selection > Cluster Curve in the Modeling NURBS guide.

Spline IK handles are ideal for posing and animating long joint chains like those for tails, tentacles, necks, spines, and
similar objects.

Start joint flipping

The start joint of your spline IK joint chain can sometimes flip when you move or rotate the spline IK curve or its CVs, or
when you slide the joint chain along its curve. The flipping is a normal result of the spline IK solver’s calculations.

Joint flipping occurs when the orientation of a joint is more than 90 degrees from its rotation value of 0. A joint’s rotation
value is 0 when its Rotate X, Y, and Z values are 0, relative to its parent joint’s rotation values. Flipping is most pronounced when a joint nears 180 degrees
rotation.

2 Bone solver

The 2 bone IK solver is a subset of the rotate plane IK solver. Therefore, IK handles with the 2 bone IK solver solve the rotations of their joint chains in the same manner as
a rotate plane IK handle. See Rotate Plane solver and Rotate Plane IK handle components.

The two bone IK handle is meant for posing and animating short joint chains that consist of three joints (two bones). If you
try to pose and animate a longer joint chain with the two bone IK handle, then the 2 bone solver will solve for the rotations
of only the start and second to last joints and will ignore all other joints in the joint chain.

The 2 bone solver is ideal for posing joint chains (such as arms and legs) that you want to stay in the same plane. For example,
the shoulder, elbow, and wrist joints of an arm driven by a rotate plane IK handle all stay within the same plane as the elbow
rotates. The plane itself can be rotated from the shoulder joint by the pole vector. See Pole vector.

The 2 bone solver is the fastest IK solver in Maya. This makes two bone IK handles ideal for setting up characters in a games
development environment. Maya includes the source code for the two bone IK solver plug-in so that game developers can replicate
the exact behavior of this feature in a games engine or modify the code to create their own custom IK solvers.

IK two bone solver plug-in source code

The source code for the two bone IK solver is available in the devkit’s ik2Bsolver directory. The source code provides an
example of how you can create your own IK solver plug-in. Also, by extracting the core algorithm, you can replicate the exact
behavior of the 2 bone IK solver in a games engine. For more information, please read the README file in the ik2Bsolver directory.

Multi-chain solver

The multi-chain solver can solve for multiple IK handles simultaneously. You can use the multi-chain IK handles to animate
complex motions such as those of the tentacles of an octopus character.

An IK handle with the multi-chain solver manages the joints in its joint chain in the same manner as a single chain IK handle. See Single Chain solver.

The spring IK solver keeps the angles between joints in its joint chain proportional by applying bias values to those angles. This ensures that the angles between all joints are always evenly distributed. The spring IK solver
is similar to the rotate plane IK solver in that both their IK handles have pole vectors. Since the spring IK handle has a pole vector, flipping will occur if the spring IK joint chain crosses its pole vector.

An IK handle using the spring IK solver requires a rest pose. By default, the position and orientation of the target joint chain at the time of the spring IK handle’s creation is its
rest pose. The distance between the first and last joint of a spring IK joint chain at its rest pose determines if the joint
chain is flexed or extended, and influences each individual joint’s movement.